15edo: Difference between revisions
Wikispaces>hstraub **Imported revision 616382865 - Original comment: ** |
Wikispaces>TallKite **Imported revision 621464903 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 21:34:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>621464903</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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=Intervals= | =Intervals= | ||
|| | ||~ Degree ||~ Cents ||~ Solfege | ||
(porcupine-based) || | (porcupine-based) ||~ Porcupine[8] | ||
(Greek) || | (Greek) ||~ Blackwood | ||
"guitar notation" || | "guitar notation" ||~ Porcupine[7] | ||
(traditional) || | (traditional) ||~ Blackwood | ||
Decimal || | Decimal ||~ Approximate Ratios* || | ||
||= 0 ||= 0 ||= do ||= α ||= E ||= G ||= 1 ||= 1/1 || | ||= 0 ||= 0 ||= do ||= α ||= E ||= G ||= 1 ||= 1/1 || | ||
||= 1 ||= 80 ||= di ||= α/ β\ ||= E# ||= G# / Abb ||= 1# / 2b ||= 25/24, 21/20, 16/15 || | ||= 1 ||= 80 ||= di ||= α/ β\ ||= E# ||= G# / Abb ||= 1# / 2b ||= 25/24, 21/20, 16/15 || | ||
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...A3 - A4 - A5 - A6 - A7 - A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 -- d8 - d2 - d3 -- d4 - d5 -- d6... | ...A3 - A4 - A5 - A6 - A7 - A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 -- d8 - d2 - d3 -- d4 - d5 -- d6... | ||
...Fx - Gx - A# - B# - C# - D# - E# - F# - G# --- A --- B --- C -- D --- E --- F --- G -- Ab -- Bb - Cb - Db - Eb - Fb - Gb - Abb - Bbb... | ...Fx - Gx - A# - B# - C# - D# - E# - F# - G# --- A --- B --- C -- D --- E --- F --- G -- Ab -- Bb - Cb - Db - Eb - Fb - Gb - Abb - Bbb... | ||
|| | ||~ step ||~ cents ||||~ ups and downs relative notation | ||
(partial list, e.g. M2 is also A1 and d4) || | (partial list, e.g. M2 is also A1 and d4) ||~ ups and downs | ||
absolute notation || | absolute notation ||~ porcupine | ||
relative notation || | relative notation ||~ porcupine | ||
absolute notation || | absolute notation || | ||
||= 0 ||= 0¢ ||= P1, m2 ||= unison, min 2nd ||= C# / D / Eb ||= unison ||= D || | ||= 0 ||= 0¢ ||= P1, m2 ||= unison, min 2nd ||= C# / D / Eb ||= unison ||= D || | ||
| Line 76: | Line 76: | ||
||= 14 ||= 1120 ||= vM7, v8 ||= downmajor 7th, down octave ||= C#v / Dv / Ebv ||= aug 7th, dim 8ve ||= C# / Db || | ||= 14 ||= 1120 ||= vM7, v8 ||= downmajor 7th, down octave ||= C#v / Dv / Ebv ||= aug 7th, dim 8ve ||= C# / Db || | ||
||= 15 ||= 1200 ||= M7, P8 ||= major 7th, octave ||= C# / D / Eb ||= 8ve ||= D || | ||= 15 ||= 1200 ||= M7, P8 ||= major 7th, octave ||= C# / D / Eb ||= 8ve ||= D || | ||
15edo | All 15edo chords can be named using ups and downs. Because many intervals have several names, many chords do too. | ||
0-3-9 = D E A = | 0-3-9 = D E A = D2 = "D sus 2", or D F A = Dm = "D minor" (approximate 6:7:9) | ||
0-4-9 = D F^ A = D.^m = "D upminor" | 0-4-9 = D F^ A = D.^m = "D upminor" (approximate 10:12:15) | ||
0-5-9 = D F#v A = D.v = "D dot down" or "D downmajor" | 0-5-9 = D F#v A = D.v = "D dot down" or "D downmajor" (approximate 4:5:6) | ||
0-6-9 = D G A = | 0-6-9 = D G A = D4, or D F# A = D = "D" or "D major" (approximate 14:18:21) | ||
0-3-9-12 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six" | 0-3-9-12 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six" | ||
0-4-9-12 = D F^ A C = Dm7(^3) = "D minor seven up-three", or D F^ A B = Dm6(^3) = "D minor six up-three" | 0-4-9-12 = D F^ A C = Dm7(^3) = "D minor seven up-three", or D F^ A B = Dm6(^3) = "D minor six up-three" | ||
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0-5-9-14 = D F#v A C#v = D.vM7 = "D downmajor seven" | 0-5-9-14 = D F#v A C#v = D.vM7 = "D downmajor seven" | ||
0-4-9-13 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six" | 0-4-9-13 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six" | ||
For a more complete list, see [[Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]] | For a more complete list, see [[Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | ||
15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by [[IgliashonJones|Igliashon Jones]] in the paper "[[http://www.cityoftheasleep.com/etc/5nEDOs.pdf|Five is Not an Odd Number]]". For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see [[@Harmony in 15edo Blacksmith|Harmony in 15edo Blacksmith[10]]]. | 15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by [[IgliashonJones|Igliashon Jones]] in the paper "[[http://www.cityoftheasleep.com/etc/5nEDOs.pdf|Five is Not an Odd Number]]". For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see [[@Harmony in 15edo Blacksmith|Harmony in 15edo Blacksmith[10]]]. | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Degree<br /> | ||
</ | </th> | ||
< | <th>Cents<br /> | ||
</ | </th> | ||
< | <th>Solfege<br /> | ||
(porcupine-based)<br /> | (porcupine-based)<br /> | ||
</ | </th> | ||
< | <th>Porcupine[8]<br /> | ||
(Greek)<br /> | (Greek)<br /> | ||
</ | </th> | ||
< | <th>Blackwood<br /> | ||
&quot;guitar notation&quot;<br /> | &quot;guitar notation&quot;<br /> | ||
</ | </th> | ||
< | <th>Porcupine[7]<br /> | ||
(traditional)<br /> | (traditional)<br /> | ||
</ | </th> | ||
< | <th>Blackwood<br /> | ||
Decimal<br /> | Decimal<br /> | ||
</ | </th> | ||
< | <th>Approximate Ratios*<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 606: | Line 606: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>step<br /> | ||
</ | </th> | ||
< | <th>cents<br /> | ||
</ | </th> | ||
< | <th colspan="2">ups and downs relative notation<br /> | ||
(partial list, e.g. M2 is also A1 and d4)<br /> | (partial list, e.g. M2 is also A1 and d4)<br /> | ||
</ | </th> | ||
< | <th>ups and downs<br /> | ||
absolute notation<br /> | absolute notation<br /> | ||
</ | </th> | ||
< | <th>porcupine<br /> | ||
relative notation<br /> | relative notation<br /> | ||
</ | </th> | ||
< | <th>porcupine<br /> | ||
absolute notation<br /> | absolute notation<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 881: | Line 881: | ||
</table> | </table> | ||
15edo | All 15edo chords can be named using ups and downs. Because many intervals have several names, many chords do too.<br /> | ||
0-3-9 = D E A = | 0-3-9 = D E A = D2 = &quot;D sus 2&quot;, or D F A = Dm = &quot;D minor&quot; (approximate 6:7:9)<br /> | ||
0-4-9 = D F^ A = D.^m = &quot;D upminor&quot;<br /> | 0-4-9 = D F^ A = D.^m = &quot;D upminor&quot; (approximate 10:12:15)<br /> | ||
0-5-9 = D F#v A = D.v = &quot;D dot down&quot; or &quot;D downmajor&quot;<br /> | 0-5-9 = D F#v A = D.v = &quot;D dot down&quot; or &quot;D downmajor&quot; (approximate 4:5:6)<br /> | ||
0-6-9 = D G A = | 0-6-9 = D G A = D4, or D F# A = D = &quot;D&quot; or &quot;D major&quot; (approximate 14:18:21)<br /> | ||
0-3-9-12 = D F A C = Dm7 = &quot;D minor seven&quot;, or D F A B = Dm6 = &quot;D minor six&quot;<br /> | 0-3-9-12 = D F A C = Dm7 = &quot;D minor seven&quot;, or D F A B = Dm6 = &quot;D minor six&quot;<br /> | ||
0-4-9-12 = D F^ A C = Dm7(^3) = &quot;D minor seven up-three&quot;, or D F^ A B = Dm6(^3) = &quot;D minor six up-three&quot;<br /> | 0-4-9-12 = D F^ A C = Dm7(^3) = &quot;D minor seven up-three&quot;, or D F^ A B = Dm6(^3) = &quot;D minor six up-three&quot;<br /> | ||
| Line 892: | Line 892: | ||
0-5-9-14 = D F#v A C#v = D.vM7 = &quot;D downmajor seven&quot;<br /> | 0-5-9-14 = D F#v A C#v = D.vM7 = &quot;D downmajor seven&quot;<br /> | ||
0-4-9-13 = D F^ A C^ = D.^m7 = &quot;D dot up minor-seven&quot;, or D F^ A B^ = D.^m6 = &quot;D dot up minor-six&quot;<br /> | 0-4-9-13 = D F^ A C^ = D.^m7 = &quot;D dot up minor-seven&quot;, or D F^ A B^ = D.^m6 = &quot;D dot up minor-six&quot;<br /> | ||
For a more complete list, see <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a> | For a more complete list, see <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br /> | ||
<br /> | <br /> | ||
15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> in the paper &quot;<a class="wiki_link_ext" href="http://www.cityoftheasleep.com/etc/5nEDOs.pdf" rel="nofollow">Five is Not an Odd Number</a>&quot;. For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see <a class="wiki_link" href="/Harmony%20in%2015edo%20Blacksmith" target="_blank">Harmony in 15edo Blacksmith[10</a>].<br /> | 15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> in the paper &quot;<a class="wiki_link_ext" href="http://www.cityoftheasleep.com/etc/5nEDOs.pdf" rel="nofollow">Five is Not an Odd Number</a>&quot;. For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see <a class="wiki_link" href="/Harmony%20in%2015edo%20Blacksmith" target="_blank">Harmony in 15edo Blacksmith[10</a>].<br /> | ||